The IEC/ISO definition of voltage gives consistent results in accordance with what is read by a voltmeter, regardless of the source of the 'electromotance'. Consider
Consider for example the following two circuits, one where the source of EMF is the lumped secondary coil of a transformer, and one where the circuit path encloses the variable magnetic region:
If you only have access to, say, one eight of the length of the copper conductor forming joining the components in a room without knowledge of what is outside, can you find the voltage between points C and D, assuming the current in the circuit is not generating a relevant dB/dt of its own (say it's 10mA at 50Hz)?
Using
Using the IEC/ISO definition of voltage you get consistent results in both cases: the IEC voltage is in both cases equal to what Ohm's law tell you, and it is also equal to what you measure with a voltmeter in your room.
Using
Using the 1800s version of voltage that is equal to scalar potential difference in the IEC notations, you cannot tell what it is unless you know whether the EMF is localized or distributed. And you can't trust your voltmeter either because it does not measure 'your'version of voltage.
References:
References:Ramo, Whinnery, VanDuzer
Ramo, Whinnery, VanDuzer, "Fields and Waves in Communication Electronics", Wiley. p. 266 in the first edition, Chapter 4 "The electromagnetics of circuits" in the second and third editions.
Purcell, MorinPurcell, Morin, "Electricity and Magnetism", Cambridge
FeynmanFeynman, "Feynman's Lectures on Physics", Addison Wesley. Volume 2 , Chapter 22.
Popovic, "Introductory Engineering Electromagnetics", p. 496
Brandão Faria, "Electromagnetic Foundations of Electrical Engineering", Wiley, p. 208